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A Generic Test of Modified Gravity Models which Emulate Dark Matter

A Generic Test of Modified Gravity Models which Emulate Dark Matter. arXiv:0705.0153 [astro-ph] with Emre Kahya. Dark Matter vs Modified Gravity. G μν =8 π G Τ μν works for solar system But not for galaxies Theory: v²=GM∕r Obs: v²~√a 0 GM Could be missing M Or modified gravity.

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A Generic Test of Modified Gravity Models which Emulate Dark Matter

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  1. A Generic Test of Modified Gravity Models which Emulate Dark Matter arXiv:0705.0153 [astro-ph] with Emre Kahya

  2. Dark Matter vs Modified Gravity • Gμν=8πGΤμνworks for solar system • But not for galaxies • Theory: v²=GM∕r • Obs: v²~√a0GM • Could be missing M • Or modified gravity

  3. ds²=-B(r)dct²+A(r)dr²+r²dΩ² • A'/(r A) + (A - 1)/r² = (A/B) 8πGρ/c² • B'/(r B) - (A - 1)/r² = 0 SphericalMassM • ε = 2GM/(c²r) • B = 1 - ε and A = 1/(1 - ε) ~ 1 + ε • ε ~ .0000006 at rs ~ 8 kpc WithIsothermalHalofor r > rs • ε* = 2√a0GM/c² • B ~ 1 – ε + ε* ln(r/rs) and A ~ 1 + ε + ε* • ε* ~ .0000006

  4. No-Go Thm for metric modelsWith Soussa, astro-ph/0307358 • Єμν= 8πG Tμν ~ GM for gμν = ημν + hμν • hμν~ v² ~√a0GM someЄμν‘s ~ h² • If allЄμν ~ h² unstable! • Distinguished subsets • Divergence (0 to all orders) • Trace conf. invariant for Єμν ~ h¹ • Extra force in conf. factor no lensing!

  5. Five Assumptions • Gravity carried by hμνwith source Tμν • General coordinate invariance • Extra force in ultra-weak field regime • Stability (forbids allЄμν ~ h²) • Light couples conformally • Known models violate (1) & (5) • Violating (4) may also work

  6. TeVeS Bekenstein (astro-ph/0403694) OK Cosmology (astro-ph/0505519, 0606216, 0608602, 0611255) SVTG Moffat (gr-qc/0506021) astro-ph/0506370 Fields: gμν, Aμ & φ Extra force from φ Matter couples to ĝμν=Exp(-2φ) gμν + 2 sinh(2φ)Aμ Aν R term for solar system Gravitons couple to gμν ĝμνfrom GR with D.M. gμνfrom GR w/o D.M. Known Models

  7. Dark Matter Emulatorsds²=-B(r)dt²+A(r)dr²+r²dΩ • Without Dark Matter, ε=2GM/(c²r) • B = 1-ε and A = 1/(1-ε) ~ 1+ε • ε ~ .0000006 for rs ~ 8 kpc • Weak gravity waves see this geometry • With Isothermal Halo, ε*=2√a0GM/c² • B ~ 1-ε+ε*ln(r/rs) and A ~ 1+ε+ε* • ε* ~ .0000006 • Ordinary matter sees this geometry

  8. Light-like Pulses from (0,xL) • Gravitons follow gμν to (t,xs) • B ~ 1 - ε and A ~ 1 + ε • ε = 2GM/(rc²) ~ .0000006 at rs ~ 8 kpc • ν's and γ's follow ĝμν to (T,xs) • B ~ 1 – ε + ε* ln((r/rs) and A ~ 1 + ε + ε* • ε* ~ 2√a0GM/c² ~.0000006 • Δt = T – t = # ε* Δx/c • SN 1987a: Δt ~ -.144 · 36.7 day ~ -5.3 day • ~ hrs diff. between ν’s and γ’s irrelevant • Advanced LIGO will see to .8 Mpc!

  9. Radial Prop: v/c = B(r)/A(r) • Gravitons: v/c ~ 1 – 2ε • ν’s & γ’s: V/c 1 - 2ε + ε* ln(r/rs) - ε* • Typically faster than gravitons • But depends on r and rs • Moore & Nelson, hep-ph/0106220 • (V-v)/c < 2 x E-15 for galaxy (maybe ok) • (V-v)/c < 2 x E-19 for extra-gal. (not ok)

  10. Conclusions • Mod. Gravity may explain rot. curves • But unstable if pure metric • Otherwise new fields and two metrics • Gravitons couple to gμν of GR w/o D.M. • Matter couples to ĝμν of GR with D.M. • Big time lag for gravitons vs ν’s & γ’s

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